Share This Article:

Amenability and the Extension Property

Abstract Full-Text HTML XML Download Download as PDF (Size:2578KB) PP. 2945-2951
DOI: 10.4236/am.2014.519279    2,506 Downloads   2,752 Views  

ABSTRACT

Let G be a locally compact group, H a closed amenable subgroup and u an element of the Herz Figà-Talamanca algebra of H with compact support, we prove the existence of an extension of u to G, with a good control of the norm and of the support of the extension.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Derighetti, A. (2014) Amenability and the Extension Property. Applied Mathematics, 5, 2945-2951. doi: 10.4236/am.2014.519279.

References

[1] Herz, C.S. (1973) Harmonic Synthesis for Subgroups. Annales de l'institut Fourier, 23, 91-123.
http://dx.doi.org/10.5802/aif.473
[2] Fiorillo, C. (2009) An Extension Property for the Figà-Talamanca Herz Algebra. Proceedings of the American Mathematical Society, 137, 1001-1011.
http://dx.doi.org/10.1090/S0002-9939-08-09679-2
[3] McMullen, J.R. (1972) Extensions of Positive-Definite Functions. Memoirs of the American Mathematical Society, 117.
[4] Delaporte, J. and Derighetti, A. (1992) On Herz’ Extension Theorem. Bollettino dell’Unime Matematica Italiana, (7) 6-A, 245-247.
[5] Reiter, H. and Stegman, J.D. (2000) Classical Harmonic Analysis and Locally Compact Groups. Clarendon Press, Oxford.
[6] Derighetti, A. (2004) On Herz’s Projection Theorem. Illinois Journal of Mathematics, 48, 463-476.
[7] Derighetti, A. (2011) Convolution Operators on Groups. Lecture Notes of the Unione Matematica Italiana, 11, Springer-Verlag, Berlin, Heidelberg.
[8] Delaporte, J. and Derighetti, A. (1995) p-Pseudomeasures and Closed Subgroups. Monatshefte für Mathematik, 119, 37-47.
http://dx.doi.org/10.1007/BF01292767

  
comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.